{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4ce367dd-6b9c-4d26-a3e2-dac9e8f7f08d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import pandas as pd "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6655224a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.6 0.6 1.2] [1. 1. 2.] [0.6 0.6 1.2]\n",
      "[0.6 0.6 1.2] [1. 1. 2.] [0.6 0.6 1.2]\n",
      "[0.6 0.6 1.2]\n"
     ]
    }
   ],
   "source": [
    "def Nesterov_corr_iteraion(x_t:np.array,\n",
    "                           y_t:np.array,\n",
    "                           z_t:np.array,\n",
    "                           grad_func:callable,\n",
    "                           learn_rate:float,\n",
    "                           alpha_t:float,\n",
    "                           func:callable):\n",
    "    # x_t,y_t,z_t:为n维array\n",
    "    # grad_func为梯度函数，func为目标函数\n",
    "    # learn_rate为学习率,alpha_t为动量参数\n",
    "    y_t_next = (1-alpha_t)*x_t + alpha_t*z_t\n",
    "    x_t_next_1 = y_t - learn_rate*grad_func(y_t)\n",
    "    x_t_next_2 = x_t - learn_rate*grad_func(x_t)\n",
    "    x_t_next = x_t_next_1 if func(x_t_next_1) <= func(x_t_next_2) else x_t_next_2\n",
    "    z_t_next = z_t-learn_rate/alpha_t*grad_func(y_t_next)\n",
    "    return x_t_next,y_t_next,z_t_next\n",
    "\n",
    "def Nesterov_iteraion(x_t:np.array,\n",
    "                      y_t:np.array,\n",
    "                      z_t:np.array,\n",
    "                      grad_func:callable,\n",
    "                      learn_rate:float,\n",
    "                      alpha_t:float,\n",
    "                      func:callable):\n",
    "    # x_t,y_t,z_t:为n维array\n",
    "    # grad_func为梯度函数，func为目标函数\n",
    "    # learn_rate为学习率,alpha_t为动量参数\n",
    "    y_t_next = (1-alpha_t)*x_t + alpha_t*z_t\n",
    "    x_t_next = y_t - learn_rate*grad_func(y_t)\n",
    "    z_t_next = z_t-learn_rate/alpha_t*grad_func(y_t_next)\n",
    "    return x_t_next,y_t_next,z_t_next\n",
    "\n",
    "def gradient_descent_iteraion(x_t:np.array,\n",
    "                             grad_func:callable,\n",
    "                             learn_rate:float,\n",
    "                             func:callable):\n",
    "    # x_t,y_t,z_t:为n维array\n",
    "    # grad_func为梯度函数，func为目标函数\n",
    "    # learn_rate为学习率,alpha_t为动量参数\n",
    "    x_t_next = x_t - learn_rate*grad_func(x_t)\n",
    "    return x_t_next\n",
    "\n",
    "def AFBM_iteraion(x_t_root:np.array,\n",
    "                  x_t:np.array,\n",
    "                  step:int,\n",
    "                  alpha_t:float,\n",
    "                  grad_func:callable,\n",
    "                  learn_rate:float,\n",
    "                  func:callable):\n",
    "    # x_t,y_t,z_t:为n维array\n",
    "    # grad_func为梯度函数，func为目标函数\n",
    "    # learn_rate为学习率,alpha_t为动量参数\n",
    "    y_t = x_t + ((step-1)/(step+alpha_t-1))*grad_func(x_t-x_t_root)\n",
    "    z_t = y_t - learn_rate*grad_func(y_t)\n",
    "    x_t_next = x_t - learn_rate*grad_func(x_t)\n",
    "    return x_t_next\n",
    "x_t = np.array([1,1,2])\n",
    "y_t = np.array([1,1,2])\n",
    "z_t = np.array([1,1,2])\n",
    "\n",
    "learn_rate = 0.2\n",
    "func = lambda x: np.sum(x**2)\n",
    "grad_func = lambda x: 2*x\n",
    "\n",
    "x_tt,y_tt,z_tt = Nesterov_corr_iteraion(x_t,y_t,z_t,grad_func,learn_rate,0.5,func)\n",
    "print(x_tt,y_tt,z_tt)\n",
    "x_tt,y_tt,z_tt = Nesterov_iteraion(x_t,y_t,z_t,grad_func,learn_rate,0.5,func)\n",
    "print(x_tt,y_tt,z_tt)\n",
    "x_tt = gradient_descent_iteraion(x_t,grad_func,learn_rate,func)\n",
    "print(x_tt)\n",
    "\n",
    "li1 = []\n",
    "for k in range(1,100):\n",
    "    alpha = 3/(k+3)\n",
    "    x_t,y_t,z_t = Nesterov_corr_iteraion(x_t,y_t,z_t,grad_func,alpha,0.5,func)\n",
    "    li1.append(func(x_t))\n",
    "\n",
    "li2 = []\n",
    "for j in range(1,100):\n",
    "    alpha = 1+2*alpha\n",
    "    x_t,y_t,z_t = Nesterov_corr_iteraion(x_t,y_t,z_t,grad_func,3/(k+3),0.5,func)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "08c8e656",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "优化后的解: [-0.  0. -0. -0.  0. -0. -0.  0.  0.  0.  0. -0.  0.  0. -0.  0.  0.  0.\n",
      "  0.  0.  0.  0. -0.  0.  0. -0.  0. -0. -0.  0.  0. -0.  0.  0. -0. -0.\n",
      " -0. -0.  0. -0. -0. -0. -0.  0.  0.  0.  0. -0.  0.  0.]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "def soft_thresholding(x, lambda_):\n",
    "    \"\"\"L1-Soft Thresholding\"\"\"\n",
    "    return np.sign(x) * np.maximum(np.abs(x) - lambda_, 0)\n",
    "\n",
    "def forward_backward(A, b, lambda_, max_iter=1000, tol=1e-6):\n",
    "    m, n = A.shape\n",
    "    x = np.zeros(n)  # 初始解\n",
    "    y = np.zeros(n)  # 中间变量\n",
    "    t = 1  # 初始加速参数\n",
    "    alpha = 1e-3  # 步长参数\n",
    "\n",
    "    # 计算初始梯度\n",
    "    grad_f = A.T @ (A @ x - b)\n",
    "\n",
    "    for k in range(max_iter):\n",
    "        # 前向步骤：计算y的更新\n",
    "        y_new = x - alpha * grad_f  # 前向更新\n",
    "        \n",
    "        # 后向步骤：对L1正则化项应用soft thresholding\n",
    "        x_new = soft_thresholding(y_new, lambda_)\n",
    "        \n",
    "        # 加速步骤：Nesterov加速\n",
    "        t_new = (1 + np.sqrt(1 + 4 * t**2)) / 2  # 计算新的加速因子\n",
    "        y_new = x_new + (t - 1) / t_new * (x_new - x)  # 加速更新\n",
    "        \n",
    "        # 更新变量\n",
    "        x = x_new\n",
    "        t = t_new\n",
    "        \n",
    "        # 计算梯度\n",
    "        grad_f = A.T @ (A @ x - b)\n",
    "\n",
    "        # 检查停止准则：如果解变化小于tol，停止迭代\n",
    "        if np.linalg.norm(x - x_new) < tol:\n",
    "            break\n",
    "\n",
    "    return x\n",
    "\n",
    "# 示例用法\n",
    "if __name__ == \"__main__\":\n",
    "    # 随机生成数据A和b\n",
    "    m, n = 100, 50\n",
    "    A = np.random.randn(m, n)\n",
    "    b = np.random.randn(m)\n",
    "    lambda_ = 0.1  # 正则化参数\n",
    "\n",
    "    # 使用加速前向-后向算法求解\n",
    "    x_opt = forward_backward(A, b, lambda_)\n",
    "    print(\"优化后的解:\", x_opt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c540fb94",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "27ae2cf4",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def alpha(k):\n",
    "    return 3/(k+3)\n",
    "\n",
    "def alpha_forward(alpha):\n",
    "    beta = 1/alpha\n",
    "    return 1/(beta**(1.5)/(beta-1)**0.5)\n",
    "\n",
    "def h_k(k):\n",
    "    return -1/(alpha(k+1)**2)+alpha(k)/alpha(k+1)**2+1/alpha(k)**2\n",
    "\n",
    "#def h_k_forward_formula(alpha):\n",
    "#    alpha_forward = 1/beta_forward(1/alpha)\n",
    "#    return -1/alpha_forward**2+alpha/alpha_forward**2+1/alpha**2,alpha_forward\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "\n",
    "#y = []\n",
    "#h = []\n",
    "#x = []\n",
    "#a = 1/4\n",
    "#for i in range(10):\n",
    "#    i = i+2\n",
    "#    h.append(h_k(i))\n",
    "#    x.append(i)\n",
    "#    value,a = h_k_forward_formula(a)\n",
    "#    print(value)\n",
    "#    y.append(value)\n",
    "\n",
    "#plt.plot(x,y)\n",
    "#plt.show()\n",
    "import numpy as np \n",
    "import pandas as pd \n",
    "def Nesterov_iteraion(x_t:np.array,\n",
    "                      y_t:np.array,\n",
    "                      z_t:np.array,\n",
    "                      grad_func:callable,\n",
    "                      learn_rate:float,\n",
    "                      alpha_t:float,\n",
    "                      func:callable):\n",
    "    # x_t,y_t,z_t:为n维array\n",
    "    # grad_func为梯度函数，func为目标函数\n",
    "    # learn_rate为学习率,alpha_t为动量参数\n",
    "    y_t_next = (1-alpha_t)*x_t + alpha_t*z_t\n",
    "    x_t_next = y_t - learn_rate*grad_func(y_t)\n",
    "    z_t_next = z_t-learn_rate/alpha_t*grad_func(y_t_next)\n",
    "    return x_t_next,y_t_next,z_t_next\n",
    "learn_rate = 0.2\n",
    "func = lambda x: np.sum(x**2)\n",
    "grad_func = lambda x: 2*x\n",
    "\n",
    "x_t = np.array([1,1,2])\n",
    "y_t = np.array([1,1,2])\n",
    "z_t = np.array([1,1,2])\n",
    "p = []\n",
    "for i in range(100):\n",
    "    x_t,y_t,z_t = Nesterov_iteraion(x_t,y_t,z_t,grad_func,learn_rate,0.2,func)\n",
    "    p.append(math.log(func(np.array(x_t))))\n",
    "plt.plot(range(100),p,label=\"alpha_1\")\n",
    "\n",
    "x_t = np.array([1,1,2])\n",
    "y_t = np.array([1,1,2])\n",
    "z_t = np.array([1,1,2])\n",
    "p = []\n",
    "for i in range(100):\n",
    "    alpha_0 = 3/(i+3)\n",
    "    x_t,y_t,z_t = Nesterov_iteraion(x_t,y_t,z_t,grad_func,learn_rate,alpha_0,func)\n",
    "    p.append(math.log(func(np.array(x_t))))\n",
    "plt.plot(range(100),p,label=\"yes_alpha\")\n",
    "\n",
    "x_t = np.array([1,1,2])\n",
    "y_t = np.array([1,1,2])\n",
    "z_t = np.array([1,1,2])\n",
    "p = []\n",
    "for i in range(100):\n",
    "    x_t,y_t,z_t = Nesterov_iteraion(x_t,y_t,z_t,grad_func,learn_rate,0.1,func)\n",
    "    p.append(math.log(func(np.array(x_t))))\n",
    "plt.plot(range(100),p,label=\"alpha_0\")\n",
    "\n",
    "x_t = np.array([1,1,2])\n",
    "y_t = np.array([1,1,2])\n",
    "z_t = np.array([1,1,2])\n",
    "p = []\n",
    "a = 1/4\n",
    "for i in range(100):\n",
    "    a = alpha_forward(a)\n",
    "    x_t,y_t,z_t = Nesterov_iteraion(x_t,y_t,z_t,grad_func,learn_rate,a,func)\n",
    "    p.append(math.log(func(np.array(x_t))))\n",
    "plt.plot(range(100),p,label=\"extra_alpha\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fd4f9d65",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "0f5ac2eb",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import load_iris\n",
    "import numpy as np\n",
    "iris = load_iris()\n",
    "y = list(iris.target)\n",
    "y_new = y\n",
    "for i in range(len(y)):\n",
    "    if y[i] == 0:\n",
    "        y_new[i] = [1,0,0]\n",
    "    elif y[i] == 1:\n",
    "        y_new[i] = [0,1,0]\n",
    "    else:\n",
    "        y_new[i] = [0,0,1]\n",
    "X = iris.data\n",
    "y = np.array(y_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "id": "80c46200",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn import datasets\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "import copy\n",
    "# 1. 加载数据并预处理\n",
    "# 加载鸢尾花数据集\n",
    "iris = datasets.load_iris()\n",
    "X = iris.data\n",
    "y = iris.target\n",
    "\n",
    "# 标准化数据\n",
    "scaler = StandardScaler()\n",
    "X = scaler.fit_transform(X)\n",
    "\n",
    "# 目标进行One-hot编码\n",
    "y_one_hot = np.zeros((y.size, y.max() + 1))\n",
    "y_one_hot[np.arange(y.size), y] = 1\n",
    "\n",
    "# 2. 拆分训练集和测试集\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y_one_hot, test_size=0.02, random_state=42)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4497a20d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import functools\n",
    "\n",
    "def record_loss(func):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0039caf1",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 定义激活函数和它们的导数\n",
    "class Sigmoid:\n",
    "    @staticmethod\n",
    "    def activate(x):\n",
    "        return 1 / (1 + np.exp(-x))\n",
    "\n",
    "    @staticmethod\n",
    "    def derivative(x):\n",
    "        return x * (1 - x)\n",
    "\n",
    "class Softmax:\n",
    "    @staticmethod\n",
    "    def activate(x):\n",
    "        exp_values = np.exp(x - np.max(x, axis=-1, keepdims=True))  # 稳定化计算，避免溢出\n",
    "        return exp_values / np.sum(exp_values, axis=-1, keepdims=True)\n",
    "\n",
    "    @staticmethod\n",
    "    def derivative(x):\n",
    "        s = x.reshape(-1, 1)\n",
    "        return np.diagflat(s) - np.dot(s, s.T)\n",
    "\n",
    "class optimizer:\n",
    "    def update_parameters(self,params,gradients):\n",
    "        pass\n",
    "\n",
    "class GradientDescentOptimizer(optimizer):\n",
    "    def __init__(self,learning_rate=0.01):\n",
    "        self.learning_rate = learning_rate\n",
    "\n",
    "    def update_parameters(self,params,gradients):\n",
    "        updated_params = []\n",
    "        for param,gradient in zip(params,gradients):\n",
    "            updated_params.append(param - self.learning_rate * gradient)\n",
    "        return updated_params\n",
    "    \n",
    "#class NesterovSpokoinyOptimizer(optimizer):\n",
    "#    def __init__(self,learning_rate=0.01):\n",
    "#        self.learning_rate = learning_rate\n",
    "#\n",
    "#    def update_parameters(self,params,gradients):\n",
    "#        updated_params = []\n",
    "#        for param,gradient in zip(params,gradients):\n",
    "#\n",
    "#            updated_params.append(param - self.learning_rate * gradient)\n",
    "#        return updated_params\n",
    "    \n",
    "# 神经网络类\n",
    "class NeuralNetwork:\n",
    "    def __init__(self, input_size, hidden_size, output_size, optimizer,learning_rate=0.1):\n",
    "        # 网络的初始化\n",
    "        np.random.seed(1)\n",
    "        self.input_size = input_size\n",
    "        self.hidden_size = hidden_size\n",
    "        self.output_size = output_size\n",
    "        self.learning_rate = learning_rate\n",
    "        self.optimizer = optimizer\n",
    "\n",
    "        # 初始化权重和偏置\n",
    "        self.weights_input_hidden = np.random.rand(input_size, hidden_size)  # 输入层到隐藏层的权重\n",
    "        self.weights_hidden_output = np.random.rand(hidden_size, output_size)  # 隐藏层到输出层的权重\n",
    "        self.bias_hidden = np.random.rand(hidden_size)  # 隐藏层偏置\n",
    "        self.bias_output = np.random.rand(output_size)  # 输出层偏置\n",
    "        \n",
    "        # 激活函数\n",
    "        self.activation = Sigmoid()\n",
    "        self.output_activation = Softmax()\n",
    "\n",
    "    def forward_propagation(self, inputs):\n",
    "\n",
    "        # 输入层到隐藏层的计算\n",
    "        hidden_layer_input = np.dot(inputs, self.weights_input_hidden) + self.bias_hidden\n",
    "        hidden_layer_output = self.activation.activate(hidden_layer_input)\n",
    "\n",
    "        # 隐藏层到输出层的计算\n",
    "        output_layer_input = np.dot(hidden_layer_output, self.weights_hidden_output) + self.bias_output\n",
    "        output_layer_output = self.output_activation.activate(output_layer_input)\n",
    "\n",
    "        return hidden_layer_output, output_layer_output\n",
    "\n",
    "    def __add__(self,other):\n",
    "        \n",
    "        temp_nn = copy.deepcopy(self)\n",
    "        temp_nn.weights_input_hidden = self.weights_input_hidden+other.weights_input_hidden  # 输入层到隐藏层的权重\n",
    "        temp_nn.weights_hidden_output = self.weights_hidden_output+other.weights_hidden_output   # 隐藏层到输出层的权重\n",
    "        temp_nn.bias_hidden = self.bias_hidden+other.bias_hidden  # 隐藏层偏置\n",
    "        temp_nn.bias_output = self.bias_output+other.bias_output  \n",
    "\n",
    "        return temp_nn\n",
    "    \n",
    "    def __mul__(self,other):\n",
    "\n",
    "        temp_nn = copy.deepcopy(self)\n",
    "        temp_nn.weights_input_hidden = self.weights_input_hidden*other # 输入层到隐藏层的权重\n",
    "        temp_nn.weights_hidden_output = self.weights_hidden_output*other   # 隐藏层到输出层的权重\n",
    "        temp_nn.bias_hidden = self.bias_hidden*other  # 隐藏层偏置\n",
    "        temp_nn.bias_output = self.bias_output*other\n",
    "\n",
    "        return temp_nn\n",
    "    \n",
    "    def backward_propagation(self, inputs, hidden_layer_output, output_layer_output, outputs):\n",
    "        # 计算输出层的误差\n",
    "        output_error = outputs - output_layer_output  # 均方误差的梯度\n",
    "        #print(output_error)\n",
    "        output = output_error  # 交叉熵的梯度与 Softmax 输出的导数在一块儿\n",
    "\n",
    "        # 计算隐藏层的误差\n",
    "        hidden_error = output.dot(self.weights_hidden_output.T)  # 输出层误差传播到隐藏层\n",
    "        hidden = hidden_error * self.activation.derivative(hidden_layer_output)\n",
    "\n",
    "        # 计算权重和偏置的梯度\n",
    "        weights_input_hidden_gradient = -np.dot(inputs.T, hidden)\n",
    "        weights_hidden_output_gradient = -np.dot(hidden_layer_output.T, output)\n",
    "        bias_hidden_gradient = -np.sum(hidden, axis=0)\n",
    "        bias_output_gradient = -np.sum(output, axis=0)\n",
    "\n",
    "        return [weights_input_hidden_gradient, weights_hidden_output_gradient, bias_hidden_gradient, bias_output_gradient]\n",
    "\n",
    "    def update_parameters(self, gradients, learning_rate=None):\n",
    "        params = [self.weights_input_hidden, self.weights_hidden_output, self.bias_hidden, self.bias_output]\n",
    "        updated_params = self.optimizer.update_parameters(params, gradients)\n",
    "        self.weights_input_hidden, self.weights_hidden_output, self.bias_hidden, self.bias_output = updated_params\n",
    "    \n",
    "    def train(self, inputs, outputs,train_option, epochs):\n",
    "        if train_option ==\"GD\":\n",
    "            #记录训练过程中的损失\n",
    "            train_loss = []\n",
    "    \n",
    "            # 训练网络\n",
    "            for epoch in range(epochs):\n",
    "    \n",
    "                # 前向传播\n",
    "                hidden_layer_output, output_layer_output = self.forward_propagation(inputs)\n",
    "    \n",
    "                # 反向传播\n",
    "                gradients = self.backward_propagation(inputs, hidden_layer_output, output_layer_output, outputs)\n",
    "    \n",
    "                # 更新参数\n",
    "                self.update_parameters(gradients)\n",
    "    \n",
    "                loss = np.mean(np.square(outputs - output_layer_output))  # 均方误差损失\n",
    "    \n",
    "                # 每 1000 个epoch输出一次损失\n",
    "                if epoch % 1000 == 0:\n",
    "                    print(f\"Epoch {epoch}, Loss: {loss}\")\n",
    "                    \n",
    "                train_loss.append(loss)\n",
    "            \n",
    "            return train_loss\n",
    "        elif train_option ==\"NSA\" or train_option ==\"NSA_plus\":\n",
    "            #记录训练过程中的损失\n",
    "            train_loss = []\n",
    "\n",
    "            nn_y = copy.deepcopy(self)\n",
    "\n",
    "            nn_x = copy.deepcopy(self)\n",
    "\n",
    "            nn_z = copy.deepcopy(self)\n",
    "            \n",
    "            # 训练网络\n",
    "            for epoch in range(epochs-1):\n",
    "\n",
    "                if epoch==0:\n",
    "                    hidden_layer_output, output_layer_output = nn_y.forward_propagation(inputs)\n",
    "                    loss = np.mean(np.square(outputs - output_layer_output))  # 均方误差损失\n",
    "                    train_loss.append(loss)\n",
    "                    \n",
    "                epoch = epoch+1\n",
    "                #alpha_t\n",
    "                alpha = 5/(epoch+5)\n",
    "\n",
    "                ###y = (1-alpha)*x+alpha*z\n",
    "                nn_y = nn_x*(1-alpha)+nn_z*alpha\n",
    "            \n",
    "                #前向传播比较损失\n",
    "                hidden_layer_output,output_layer_output_y = nn_y.forward_propagation(inputs)\n",
    "                loss_y = np.mean(np.square(outputs - output_layer_output_y))\n",
    "                hidden_layer_output,output_layer_output_x = nn_x.forward_propagation(inputs)\n",
    "                loss_x = np.mean(np.square(outputs - output_layer_output_x))\n",
    "\n",
    "                #print(\"B\",loss_x,loss_y)\n",
    "                if train_option ==\"NSA\":\n",
    "                    ## x = y-eta*grad(y)\n",
    "                    # 前向传播\n",
    "                    hidden_layer_output, output_layer_output = nn_y.forward_propagation(inputs)\n",
    "\n",
    "                    # 反向传播\n",
    "                    y_gradients = nn_y.backward_propagation(inputs, hidden_layer_output, output_layer_output, outputs)\n",
    "        \n",
    "                    #将nn_y的参数赋值给nn_x\n",
    "                    nn_x = copy.deepcopy(nn_y)\n",
    "\n",
    "                    #更新nn_x参数\n",
    "                    nn_x.update_parameters(y_gradients)\n",
    "                elif train_option ==\"NSA_plus\":\n",
    "                    ## x1 = y-eta*grad(y)\n",
    "                    # 前向传播\n",
    "                    hidden_layer_output, output_layer_output = nn_y.forward_propagation(inputs)\n",
    "\n",
    "                    # 反向传播\n",
    "                    y_gradients = nn_y.backward_propagation(inputs, hidden_layer_output, output_layer_output, outputs)\n",
    "                    \n",
    "                    #梯度下降更新nn_y参数\n",
    "                    nn_y.update_parameters(y_gradients)\n",
    "                    \n",
    "                    ## x2 = x-eta*grad(x)\n",
    "                    # 前向传播\n",
    "                    hidden_layer_output, output_layer_output = nn_x.forward_propagation(inputs)\n",
    "\n",
    "                    # 反向传播\n",
    "                    x_gradients = nn_x.backward_propagation(inputs, hidden_layer_output, output_layer_output, outputs)\n",
    "                    \n",
    "                    #梯度下降更新nn_y参数\n",
    "                    nn_x.update_parameters(x_gradients)\n",
    "\n",
    "                    #前向传播比较损失\n",
    "                    hidden_layer_output,output_layer_output_y = nn_y.forward_propagation(inputs)\n",
    "                    loss_y = np.mean(np.square(outputs - output_layer_output_y))\n",
    "\n",
    "                    hidden_layer_output,output_layer_output_x = nn_x.forward_propagation(inputs)\n",
    "                    loss_x = np.mean(np.square(outputs - output_layer_output_x))\n",
    "                    \n",
    "                    #print(\"C\",loss_x,loss_y)\n",
    "                    if loss_y<loss_x:\n",
    "                        nn_x = copy.deepcopy(nn_y)\n",
    "                    elif loss_x<=loss_y:\n",
    "                        nn_x = copy.deepcopy(nn_x)\n",
    "\n",
    "                    hidden_layer_output,output_layer_output_x = nn_x.forward_propagation(inputs)\n",
    "                    loss_x = np.mean(np.square(outputs - output_layer_output_x))\n",
    "                    #print(\"D\",loss_x,loss_y)\n",
    "                    \n",
    "\n",
    "                ###z = z-eta/alpha*grad(y)\n",
    "                new_y_gradients = [item/alpha for item in y_gradients]\n",
    "                nn_z.update_parameters(new_y_gradients)\n",
    "\n",
    "                self = copy.deepcopy(nn_x)\n",
    "                # 前向传播计算当前损失\n",
    "                hidden_layer_output, output_layer_output = self.forward_propagation(inputs)\n",
    "                \n",
    "                loss = np.mean(np.square(outputs - output_layer_output))  # 均方误差损失\n",
    "    \n",
    "                # 每 1000 个epoch输出一次损失\n",
    "                #print(f\"Epoch {epoch}, Loss: {loss}\")\n",
    "                    \n",
    "                train_loss.append(loss)\n",
    "            return train_loss,self\n",
    "\n",
    "    def predict(self, inputs):\n",
    "        # 预测函数\n",
    "        _, predicted_output = self.forward_propagation(inputs)\n",
    "        return predicted_output"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 291,
   "id": "f9113f9f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0, Loss: 0.26119357499848134\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#实验1\n",
    "# 3. 初始化神经网络\n",
    "input_size = X_train.shape[1]  # 输入层大小（特征数量）\n",
    "hidden_size = 5  # 隐藏层大小\n",
    "output_size = y_train.shape[1]  # 输出层大小（三个类别）\n",
    "learning_rate = 0.08 # 学习率\n",
    "max_epochs = 40\n",
    "optimizer = GradientDescentOptimizer(learning_rate)\n",
    "\n",
    "# 4. 训练神经网络\n",
    "nn_NSA_plus = NeuralNetwork(input_size, hidden_size, output_size,optimizer, learning_rate)\n",
    "train_loss_NSA_plus,nn_NSA_plus = nn_NSA_plus.train(X_train, y_train,\"NSA_plus\", epochs=max_epochs)\n",
    "\n",
    "nn_NSA = NeuralNetwork(input_size, hidden_size, output_size,optimizer, learning_rate)\n",
    "train_loss_NSA,nn_NSA = nn_NSA.train(X_train, y_train,\"NSA\", epochs=max_epochs)\n",
    "\n",
    "nn_GD = NeuralNetwork(input_size, hidden_size, output_size,optimizer, learning_rate)\n",
    "train_loss_GD = nn_GD.train(X_train, y_train,\"GD\", epochs=max_epochs)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import numpy as np\n",
    "import math\n",
    "ind = 500\n",
    "# 创建一个示例数据\n",
    "y0 = [math.log(item) for item in train_loss_NSA_plus[0:ind]]\n",
    "y1 = [math.log(item) for item in train_loss_NSA[0:ind]]\n",
    "y2 = [math.log(item) for item in train_loss_GD[0:ind]]\n",
    "x = [i for i,item in enumerate(y1)][0:ind]\n",
    "\n",
    "\n",
    "# 使用 seaborn 设置美化参数\n",
    "sns.set(style=\"whitegrid\")\n",
    "\n",
    "# 创建一个新的图形\n",
    "plt.figure(figsize=(10, 6))\n",
    "\n",
    "# 绘制折线图\n",
    "plt.plot(x, y0, color='yellow', linewidth=2, linestyle='-', marker='o', markersize=5, markerfacecolor='yellow', markeredgecolor='yellow',label=\"NSA_plus\")\n",
    "plt.plot(x, y1, color='blue', linewidth=2, linestyle='-', marker='o', markersize=5, markerfacecolor='blue', markeredgecolor='blue',label=\"NSA\")\n",
    "plt.plot(x, y2, color='red', linewidth=2, linestyle='-', marker='o', markersize=5, markerfacecolor='red', markeredgecolor='red',label=\"GD\")\n",
    "\n",
    "# 添加标题和标签\n",
    "plt.title('Loss Function', fontsize=20)\n",
    "plt.xlabel('X', fontsize=14)\n",
    "plt.ylabel('Y', fontsize=14)\n",
    "\n",
    "# 显示网格\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "# 显示图形\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 292,
   "id": "2f732b2f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 0, Loss: 0.26119357499848134\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#实验2\n",
    "# 3. 初始化神经网络\n",
    "input_size = X_train.shape[1]  # 输入层大小（特征数量）\n",
    "hidden_size = 5  # 隐藏层大小\n",
    "output_size = y_train.shape[1]  # 输出层大小（三个类别）\n",
    "learning_rate = 0.07 # 学习率\n",
    "max_epochs = 350\n",
    "optimizer = GradientDescentOptimizer(learning_rate)\n",
    "\n",
    "# 4. 训练神经网络\n",
    "nn_NSA_plus = NeuralNetwork(input_size, hidden_size, output_size,optimizer, learning_rate)\n",
    "train_loss_NSA_plus,nn_NSA_plus = nn_NSA_plus.train(X_train, y_train,\"NSA_plus\", epochs=max_epochs)\n",
    "\n",
    "nn_NSA = NeuralNetwork(input_size, hidden_size, output_size,optimizer, learning_rate)\n",
    "train_loss_NSA,nn_NSA = nn_NSA.train(X_train, y_train,\"NSA\", epochs=max_epochs)\n",
    "\n",
    "nn_GD = NeuralNetwork(input_size, hidden_size, output_size,optimizer, learning_rate)\n",
    "train_loss_GD = nn_GD.train(X_train, y_train,\"GD\", epochs=max_epochs)\n",
    "\n",
    "ind = 1000\n",
    "# 创建一个示例数据\n",
    "y0 = [math.log(item) for item in train_loss_NSA_plus[0:ind]]\n",
    "y1 = [math.log(item) for item in train_loss_NSA[0:ind]]\n",
    "y2 = [math.log(item) for item in train_loss_GD[0:ind]]\n",
    "x = [i for i,item in enumerate(y1)][0:ind]\n",
    "\n",
    "\n",
    "# 使用 seaborn 设置美化参数\n",
    "sns.set(style=\"whitegrid\")\n",
    "\n",
    "# 创建一个新的图形\n",
    "plt.figure(figsize=(10, 6))\n",
    "\n",
    "# 绘制折线图\n",
    "plt.plot(x, y0, color='yellow', linewidth=2, linestyle='-', marker='o', markersize=5, markerfacecolor='yellow', markeredgecolor='yellow',label=\"NSA_plus\")\n",
    "plt.plot(x, y1, color='blue', linewidth=2, linestyle='-', marker='o', markersize=5, markerfacecolor='blue', markeredgecolor='blue',label=\"NSA\")\n",
    "plt.plot(x, y2, color='red', linewidth=2, linestyle='-', marker='o', markersize=5, markerfacecolor='red', markeredgecolor='red',label=\"GD\")\n",
    "\n",
    "# 添加标题和标签\n",
    "plt.title('Loss Function', fontsize=20)\n",
    "plt.xlabel('X', fontsize=14)\n",
    "plt.ylabel('Y', fontsize=14)\n",
    "\n",
    "# 显示网格\n",
    "plt.grid(True)\n",
    "plt.legend()\n",
    "# 显示图形\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "id": "7b3d1e19",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.010880847203468408\n",
      "0.01044923281368946\n",
      "0.03252158074900552\n"
     ]
    }
   ],
   "source": [
    "print(np.mean(np.square(y_train - nn_NSA_plus.predict(X_train))))\n",
    "print(np.mean(np.square(y_train - nn_NSA.predict(X_train))))\n",
    "print(np.mean(np.square(y_train - nn_GD.predict(X_train))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 273,
   "id": "5efdfc00",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "测试集模型准确率: 100.00%\n",
      "\n",
      "训练集模型准确率: 98.64%\n"
     ]
    }
   ],
   "source": [
    "predictions_test = nn_NSA_plus.predict(X_test)\n",
    "predicted_classes_test = np.argmax(predictions_test, axis=1)\n",
    "true_classes_test = np.argmax(y_test, axis=1)\n",
    "print(f\"\\n测试集模型准确率: {np.mean(predicted_classes_test == true_classes_test) * 100:.2f}%\")\n",
    "\n",
    "predicteds_train = nn_NSA_plus.predict(X_train)\n",
    "predicted_classes_train = np.argmax(predicteds_train, axis=1)\n",
    "true_classes_train = np.argmax(y_train,axis=1)\n",
    "print(f\"\\n训练集模型准确率: {np.mean(predicted_classes_train == true_classes_train) * 100:.2f}%\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0298be71",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "178f7875",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "713aa6b1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "tr1 =  train_loss\n",
    "print(tr1)"
   ]
  }
 ],
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